Variable Selection In Single-index Models Via Adaptive LASSO

Single-index models generalize linear regression which have applications to a variety of fields,such as discrete choice analysis in econometrics and does response models in bio-metrics,This model has both the good explanatory ability of parametric model and the flexibility of non-parametric model,which can effectively reduce the model deviation and avoid the multivariate non-parametric dimension disaster.In this essay,we will provide a way to select variable of single-index models,which is an adaptive LASSO penalized least squares approach.Compared to other traditional variable selection methods,we estimate parameters which we want globally.When the dimension of parameters in the single in-dex model is a fixed constant,under some regularity conditions,we demonstrate that the proposed estimators for parameters have the so-called Oracle property,and further more we establish the asymptotic normality and develop a sandwich formula to estimate the s-tandard deviations of the proposed estimators.Simulation studies and a real data analysis are presented to illustrate the proposed methods.